Divergence-driven co-evolution between spatial regulation and urban development in complex urban systems

Abstract Complex urban systems are shaped by the ongoing interaction between regulatory rules and emergent spatial dynamics. In planning theory and urban modelling, regulation is often conceptualized as an external instrument designed to steer or correct self-organizing processes. This paper challenges that separation by reconceptualizing regulation as an endogenous process generated within the dynamics it seeks to govern. The paper introduces a divergence-driven framework in which regulation evolves through the persistent gap between regulatory intentions and realized spatial outcomes. Rather than being treated only as policy failure, divergence is understood as a generative condition that produces recursive feedback between regulation and urban development. By developing a formal representation of this process, the paper shows how regulatory adjustment and urban dynamics may co-evolve through ongoing interaction. The contribution is primarily theoretical and methodological, offering a formal account of regulation as endogenous feedback and reframing divergence as a structural driver of adaptive governance in complex urban systems. This perspective shifts the focus from the pursuit of control and equilibrium toward the management of uncertainty and persistent misalignment.